Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences
arXiv:solv-int/9705013 · doi:10.1016/S0393-0440(97)00034-X
Abstract
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of twistor theory, such as twistor lines and twistor surfaces. A more geometric approach can be developed in a Hamilton-Jacobi formalism of Gibbons and Kodama. AMS Subject Classifiation (1991): 35Q20, 58F07,70H99
20 pages, latex, no figures